<!DOCTYPE html>
<html lang="en-US">
  <head>
    <meta charset="utf-8">
    <meta name="viewport" content="width=device-width,initial-scale=1">
    <title>DFS/BFS和图论『模板』 | whoway</title>
    <meta name="description" content="Personal Blog Website">
    <link rel="icon" href="/images/photo.jpg">
  <link rel="manifest" href="/images/photo.jpg">
  <link rel="apple-touch-icon" href="/images/photo.jpg">
  <meta http-quiv="pragma" cotent="no-cache">
  <meta http-quiv="pragma" cotent="no-cache,must-revalidate">
  <meta http-quiv="expires" cotent="0">
    
    <link rel="preload" href="/assets/css/0.styles.0dbae9ec.css" as="style"><link rel="preload" href="/assets/js/app.c70e21ad.js" as="script"><link rel="preload" href="/assets/js/62.76f4b01f.js" as="script"><link rel="prefetch" href="/assets/js/10.15222a53.js"><link rel="prefetch" href="/assets/js/100.7e0e5a86.js"><link rel="prefetch" href="/assets/js/101.efd59f25.js"><link rel="prefetch" href="/assets/js/102.dfbdc06c.js"><link rel="prefetch" href="/assets/js/103.d3ab2109.js"><link rel="prefetch" href="/assets/js/104.117957ef.js"><link rel="prefetch" href="/assets/js/105.046e8ff3.js"><link rel="prefetch" href="/assets/js/106.aebdc17d.js"><link rel="prefetch" href="/assets/js/107.248733c2.js"><link rel="prefetch" href="/assets/js/108.a2fecadc.js"><link rel="prefetch" href="/assets/js/109.35196857.js"><link rel="prefetch" href="/assets/js/11.770642f2.js"><link rel="prefetch" href="/assets/js/110.cf3d973c.js"><link rel="prefetch" href="/assets/js/111.f985889a.js"><link rel="prefetch" href="/assets/js/112.ad614f41.js"><link rel="prefetch" href="/assets/js/113.f666653c.js"><link rel="prefetch" href="/assets/js/114.c6c3f384.js"><link rel="prefetch" href="/assets/js/115.e51d3c2f.js"><link rel="prefetch" href="/assets/js/116.4f4b39f5.js"><link rel="prefetch" href="/assets/js/117.99352e11.js"><link rel="prefetch" href="/assets/js/118.c6ae6572.js"><link rel="prefetch" href="/assets/js/119.4ccbe778.js"><link rel="prefetch" href="/assets/js/12.042a92ff.js"><link rel="prefetch" href="/assets/js/120.edda1c4f.js"><link rel="prefetch" href="/assets/js/121.30a638ed.js"><link rel="prefetch" href="/assets/js/122.6efcefb1.js"><link rel="prefetch" href="/assets/js/123.91e6665b.js"><link rel="prefetch" href="/assets/js/124.f27e3d7e.js"><link rel="prefetch" href="/assets/js/125.c75712d5.js"><link rel="prefetch" href="/assets/js/126.ed756cce.js"><link rel="prefetch" href="/assets/js/127.2f06c74c.js"><link rel="prefetch" href="/assets/js/128.d5f6f30e.js"><link rel="prefetch" href="/assets/js/129.508b7eed.js"><link rel="prefetch" href="/assets/js/13.b5280c37.js"><link rel="prefetch" href="/assets/js/130.dc05f9aa.js"><link rel="prefetch" href="/assets/js/131.e0ba69b1.js"><link rel="prefetch" href="/assets/js/132.d79bcaa4.js"><link rel="prefetch" href="/assets/js/133.34acc01a.js"><link rel="prefetch" href="/assets/js/134.dabf64d5.js"><link rel="prefetch" href="/assets/js/135.ad90c915.js"><link rel="prefetch" href="/assets/js/136.dbb0074f.js"><link rel="prefetch" href="/assets/js/137.284ad365.js"><link rel="prefetch" href="/assets/js/138.a4b6856f.js"><link rel="prefetch" href="/assets/js/139.c9c1e20f.js"><link rel="prefetch" href="/assets/js/14.df02ba38.js"><link rel="prefetch" href="/assets/js/140.8b0a9269.js"><link rel="prefetch" href="/assets/js/141.9c7759c5.js"><link rel="prefetch" href="/assets/js/142.a4201a82.js"><link rel="prefetch" href="/assets/js/143.d7da6e8c.js"><link rel="prefetch" href="/assets/js/144.5e48e65d.js"><link rel="prefetch" href="/assets/js/145.a0e2633c.js"><link rel="prefetch" href="/assets/js/146.3c775f9b.js"><link rel="prefetch" href="/assets/js/147.22add89a.js"><link rel="prefetch" href="/assets/js/148.cfde1009.js"><link rel="prefetch" href="/assets/js/149.ffc835b5.js"><link rel="prefetch" href="/assets/js/15.fbdfc4ee.js"><link rel="prefetch" href="/assets/js/150.406c4b20.js"><link rel="prefetch" href="/assets/js/151.b2040eea.js"><link rel="prefetch" href="/assets/js/152.7bc65661.js"><link rel="prefetch" href="/assets/js/153.1d7c65e3.js"><link rel="prefetch" href="/assets/js/154.1309de49.js"><link rel="prefetch" href="/assets/js/155.81d3ee1f.js"><link rel="prefetch" href="/assets/js/156.154a4ef2.js"><link rel="prefetch" href="/assets/js/16.e5eb6147.js"><link rel="prefetch" href="/assets/js/17.57853c4a.js"><link rel="prefetch" href="/assets/js/18.cb9d7518.js"><link rel="prefetch" href="/assets/js/19.f354dc47.js"><link rel="prefetch" href="/assets/js/2.570d8a23.js"><link rel="prefetch" href="/assets/js/20.b5af7fad.js"><link rel="prefetch" href="/assets/js/21.0b1928fe.js"><link rel="prefetch" href="/assets/js/22.f78666de.js"><link rel="prefetch" href="/assets/js/23.29c3f366.js"><link rel="prefetch" href="/assets/js/24.6f596516.js"><link rel="prefetch" href="/assets/js/25.14067b60.js"><link rel="prefetch" href="/assets/js/26.74ba4989.js"><link rel="prefetch" href="/assets/js/27.13d60edd.js"><link rel="prefetch" href="/assets/js/28.9523cb32.js"><link rel="prefetch" href="/assets/js/29.8ec842e9.js"><link rel="prefetch" href="/assets/js/3.3fb3d2e0.js"><link rel="prefetch" href="/assets/js/30.805597a8.js"><link rel="prefetch" href="/assets/js/31.831b195d.js"><link rel="prefetch" href="/assets/js/32.063c672d.js"><link rel="prefetch" href="/assets/js/33.6d93fac3.js"><link rel="prefetch" href="/assets/js/34.56e8263c.js"><link rel="prefetch" href="/assets/js/35.dbe688bb.js"><link rel="prefetch" href="/assets/js/36.dc5af2c1.js"><link rel="prefetch" href="/assets/js/37.0a7494f6.js"><link rel="prefetch" href="/assets/js/38.fe4fc171.js"><link rel="prefetch" href="/assets/js/39.f5ed5e92.js"><link rel="prefetch" href="/assets/js/4.2c405ec8.js"><link rel="prefetch" href="/assets/js/40.fe7e2714.js"><link rel="prefetch" href="/assets/js/41.30b0811d.js"><link rel="prefetch" href="/assets/js/42.76f52d62.js"><link rel="prefetch" href="/assets/js/43.e7bb0817.js"><link rel="prefetch" href="/assets/js/44.ead0e883.js"><link rel="prefetch" href="/assets/js/45.235df046.js"><link rel="prefetch" href="/assets/js/46.5f09e829.js"><link rel="prefetch" href="/assets/js/47.67116354.js"><link rel="prefetch" href="/assets/js/48.31f34543.js"><link rel="prefetch" href="/assets/js/49.10b5ebba.js"><link rel="prefetch" href="/assets/js/5.6f47322c.js"><link rel="prefetch" href="/assets/js/50.c0f0b7f1.js"><link rel="prefetch" href="/assets/js/51.5143f3bf.js"><link rel="prefetch" href="/assets/js/52.eeddfd48.js"><link rel="prefetch" href="/assets/js/53.eb790db5.js"><link rel="prefetch" href="/assets/js/54.8fe5421c.js"><link rel="prefetch" href="/assets/js/55.d8f9004b.js"><link rel="prefetch" href="/assets/js/56.62ac9b92.js"><link rel="prefetch" href="/assets/js/57.a9caec0d.js"><link rel="prefetch" href="/assets/js/58.f93fc522.js"><link rel="prefetch" href="/assets/js/59.a81a03aa.js"><link rel="prefetch" href="/assets/js/6.8c2ea393.js"><link rel="prefetch" href="/assets/js/60.ab782775.js"><link rel="prefetch" href="/assets/js/61.6dd12daf.js"><link rel="prefetch" href="/assets/js/63.6f8a4742.js"><link rel="prefetch" href="/assets/js/64.6f8bb1fa.js"><link rel="prefetch" href="/assets/js/65.4120a44b.js"><link rel="prefetch" href="/assets/js/66.360c2d2b.js"><link rel="prefetch" href="/assets/js/67.26f84d32.js"><link rel="prefetch" href="/assets/js/68.68f45e5e.js"><link rel="prefetch" href="/assets/js/69.e311eb56.js"><link rel="prefetch" href="/assets/js/7.6762b2d7.js"><link rel="prefetch" href="/assets/js/70.cea82674.js"><link rel="prefetch" href="/assets/js/71.783ddcf7.js"><link rel="prefetch" href="/assets/js/72.e5467385.js"><link rel="prefetch" href="/assets/js/73.b8fb681b.js"><link rel="prefetch" href="/assets/js/74.1bae37db.js"><link rel="prefetch" href="/assets/js/75.024387e5.js"><link rel="prefetch" href="/assets/js/76.a8e53010.js"><link rel="prefetch" href="/assets/js/77.8c55500a.js"><link rel="prefetch" href="/assets/js/78.7ce90bf5.js"><link rel="prefetch" href="/assets/js/79.ef71713f.js"><link rel="prefetch" href="/assets/js/8.788a6364.js"><link rel="prefetch" href="/assets/js/80.acad589d.js"><link rel="prefetch" href="/assets/js/81.02670d10.js"><link rel="prefetch" href="/assets/js/82.53b7b1ac.js"><link rel="prefetch" href="/assets/js/83.99eb8581.js"><link rel="prefetch" href="/assets/js/84.d1535ce3.js"><link rel="prefetch" href="/assets/js/85.fe2b7de9.js"><link rel="prefetch" href="/assets/js/86.41850272.js"><link rel="prefetch" href="/assets/js/87.1cdc6df9.js"><link rel="prefetch" href="/assets/js/88.01bf3461.js"><link rel="prefetch" href="/assets/js/89.17c69819.js"><link rel="prefetch" href="/assets/js/9.3813842d.js"><link rel="prefetch" href="/assets/js/90.f6ae7e35.js"><link rel="prefetch" href="/assets/js/91.507bc284.js"><link rel="prefetch" href="/assets/js/92.90551782.js"><link rel="prefetch" href="/assets/js/93.dc442d78.js"><link rel="prefetch" href="/assets/js/94.315f4e94.js"><link rel="prefetch" href="/assets/js/95.ccd6c6bf.js"><link rel="prefetch" href="/assets/js/96.0c6d89d0.js"><link rel="prefetch" href="/assets/js/97.1a9f10a9.js"><link rel="prefetch" href="/assets/js/98.43be3caa.js"><link rel="prefetch" href="/assets/js/99.54c8207b.js">
    <link rel="stylesheet" href="/assets/css/0.styles.0dbae9ec.css">
  </head>
  <body>
    <div id="app" data-server-rendered="true"><div class="theme-container"><header class="navbar"><div class="sidebar-button"><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" role="img" viewBox="0 0 448 512" class="icon"><path fill="currentColor" d="M436 124H12c-6.627 0-12-5.373-12-12V80c0-6.627 5.373-12 12-12h424c6.627 0 12 5.373 12 12v32c0 6.627-5.373 12-12 12zm0 160H12c-6.627 0-12-5.373-12-12v-32c0-6.627 5.373-12 12-12h424c6.627 0 12 5.373 12 12v32c0 6.627-5.373 12-12 12zm0 160H12c-6.627 0-12-5.373-12-12v-32c0-6.627 5.373-12 12-12h424c6.627 0 12 5.373 12 12v32c0 6.627-5.373 12-12 12z"></path></svg></div> <a href="/" class="home-link router-link-active"><!----> <span class="site-name">whoway</span></a> <div class="links" style="max-width:nullpx;"><div class="search-box"><input aria-label="Search" autocomplete="off" spellcheck="false" value=""> <!----></div> <nav class="nav-links can-hide"><div class="nav-item"><div class="dropdown-wrapper"><a class="dropdown-title"><span class="title">🎓Coding</span> <span class="arrow right"></span></a> <ul class="nav-dropdown" style="display:none;"><li class="dropdown-item"><!----> <a href="/00.Coding/TheBeautyOfProgramming/" class="nav-link">🔖编程之美题解</a></li><li class="dropdown-item"><!----> <a href="/00.Coding/CodeWarehouse/" class="nav-link">🔖代码意识流</a></li></ul></div></div><div class="nav-item"><div class="dropdown-wrapper"><a class="dropdown-title"><span class="title">🚀语言</span> <span class="arrow right"></span></a> <ul class="nav-dropdown" style="display:none;"><li class="dropdown-item"><!----> <a href="/01.Language/Overview/" class="nav-link">🔖概述</a></li><li class="dropdown-item"><!----> <a href="/01.Language/C/" class="nav-link">⭐️C</a></li><li class="dropdown-item"><!----> <a href="/01.Language/Cpp/" class="nav-link">🚀C++</a></li><li class="dropdown-item"><!----> <a href="/01.Language/Java/" class="nav-link">☕️Java</a></li><li class="dropdown-item"><!----> <a href="/01.Language/Python/" class="nav-link">🧩Python3</a></li></ul></div></div><div class="nav-item"><a href="/02.Hardware/" class="nav-link">✔️硬件基础</a></div><div class="nav-item"><div class="dropdown-wrapper"><a class="dropdown-title"><span class="title">⭐️软件基础</span> <span class="arrow right"></span></a> <ul class="nav-dropdown" style="display:none;"><li class="dropdown-item"><!----> <a href="/03.Software/01.DataStructureAndAlgorithm/" class="nav-link router-link-active">🐾数据结构和算法</a></li><li class="dropdown-item"><!----> <a href="/03.Software/02.OS/" class="nav-link">💻操作系统</a></li><li class="dropdown-item"><!----> <a href="/03.Software/03.Net/" class="nav-link">☁️计算机网络</a></li><li class="dropdown-item"><!----> <a href="/03.Software/04.SE/" class="nav-link">✅软件工程</a></li></ul></div></div><div class="nav-item"><a href="/04.Database/" class="nav-link">🎨数据库</a></div><div class="nav-item"><a href="/05.Engineer/" class="nav-link">🔖学术/工程</a></div><div class="nav-item"><div class="dropdown-wrapper"><a class="dropdown-title"><span class="title">⚙️工具</span> <span class="arrow right"></span></a> <ul class="nav-dropdown" style="display:none;"><li class="dropdown-item"><!----> <a href="/06.Tools/01.employment/" class="nav-link">🔖求职</a></li><li class="dropdown-item"><!----> <a href="/06.Tools/02.efficiency/" class="nav-link">🚀效能</a></li><li class="dropdown-item"><!----> <a href="/06.Tools/03.windows/" class="nav-link">⚙️Windows</a></li><li class="dropdown-item"><!----> <a href="/06.Tools/04.design/" class="nav-link">🧩设计</a></li><li class="dropdown-item"><!----> <a href="/06.Tools/05.linux/" class="nav-link">🐉Linux</a></li></ul></div></div><div class="nav-item"><a href="https://github.com/whoway" target="_blank" rel="noopener noreferrer" class="nav-link external">
  GitHub
  <svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg></a></div> <!----></nav></div></header> <div class="sidebar-mask"></div> <div class="sidebar"><nav class="nav-links"><div class="nav-item"><div class="dropdown-wrapper"><a class="dropdown-title"><span class="title">🎓Coding</span> <span class="arrow right"></span></a> <ul class="nav-dropdown" style="display:none;"><li class="dropdown-item"><!----> <a href="/00.Coding/TheBeautyOfProgramming/" class="nav-link">🔖编程之美题解</a></li><li class="dropdown-item"><!----> <a href="/00.Coding/CodeWarehouse/" class="nav-link">🔖代码意识流</a></li></ul></div></div><div class="nav-item"><div class="dropdown-wrapper"><a class="dropdown-title"><span class="title">🚀语言</span> <span class="arrow right"></span></a> <ul class="nav-dropdown" style="display:none;"><li class="dropdown-item"><!----> <a href="/01.Language/Overview/" class="nav-link">🔖概述</a></li><li class="dropdown-item"><!----> <a href="/01.Language/C/" class="nav-link">⭐️C</a></li><li class="dropdown-item"><!----> <a href="/01.Language/Cpp/" class="nav-link">🚀C++</a></li><li class="dropdown-item"><!----> <a href="/01.Language/Java/" class="nav-link">☕️Java</a></li><li class="dropdown-item"><!----> <a href="/01.Language/Python/" class="nav-link">🧩Python3</a></li></ul></div></div><div class="nav-item"><a href="/02.Hardware/" class="nav-link">✔️硬件基础</a></div><div class="nav-item"><div class="dropdown-wrapper"><a class="dropdown-title"><span class="title">⭐️软件基础</span> <span class="arrow right"></span></a> <ul class="nav-dropdown" style="display:none;"><li class="dropdown-item"><!----> <a href="/03.Software/01.DataStructureAndAlgorithm/" class="nav-link router-link-active">🐾数据结构和算法</a></li><li class="dropdown-item"><!----> <a href="/03.Software/02.OS/" class="nav-link">💻操作系统</a></li><li class="dropdown-item"><!----> <a href="/03.Software/03.Net/" class="nav-link">☁️计算机网络</a></li><li class="dropdown-item"><!----> <a href="/03.Software/04.SE/" class="nav-link">✅软件工程</a></li></ul></div></div><div class="nav-item"><a href="/04.Database/" class="nav-link">🎨数据库</a></div><div class="nav-item"><a href="/05.Engineer/" class="nav-link">🔖学术/工程</a></div><div class="nav-item"><div class="dropdown-wrapper"><a class="dropdown-title"><span class="title">⚙️工具</span> <span class="arrow right"></span></a> <ul class="nav-dropdown" style="display:none;"><li class="dropdown-item"><!----> <a href="/06.Tools/01.employment/" class="nav-link">🔖求职</a></li><li class="dropdown-item"><!----> <a href="/06.Tools/02.efficiency/" class="nav-link">🚀效能</a></li><li class="dropdown-item"><!----> <a href="/06.Tools/03.windows/" class="nav-link">⚙️Windows</a></li><li class="dropdown-item"><!----> <a href="/06.Tools/04.design/" class="nav-link">🧩设计</a></li><li class="dropdown-item"><!----> <a href="/06.Tools/05.linux/" class="nav-link">🐉Linux</a></li></ul></div></div><div class="nav-item"><a href="https://github.com/whoway" target="_blank" rel="noopener noreferrer" class="nav-link external">
  GitHub
  <svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg></a></div> <!----></nav>  <ul class="sidebar-links"><li><div class="sidebar-group first"><p class="sidebar-heading open"><span>DFS/BFS和图论『模板』</span> <!----></p> <ul class="sidebar-group-items"><li><a href="/03.Software/01.DataStructureAndAlgorithm/SkillLibrary/Part03.DFS%E5%92%8CBFS%E5%92%8C%E5%9B%BE%E8%AE%BA%E6%8A%80%E5%B7%A7.html#📑-目录" class="sidebar-link">📑 目录</a><ul class="sidebar-sub-headers"></ul></li><li><a href="/03.Software/01.DataStructureAndAlgorithm/SkillLibrary/Part03.DFS%E5%92%8CBFS%E5%92%8C%E5%9B%BE%E8%AE%BA%E6%8A%80%E5%B7%A7.html#_01-dfs模板⭐️" class="sidebar-link">01.DFS模板⭐️</a><ul class="sidebar-sub-headers"><li class="sidebar-sub-header"><a href="/03.Software/01.DataStructureAndAlgorithm/SkillLibrary/Part03.DFS%E5%92%8CBFS%E5%92%8C%E5%9B%BE%E8%AE%BA%E6%8A%80%E5%B7%A7.html#_1-1-邻接矩阵版（递归写法）" class="sidebar-link">1.1.邻接矩阵版（递归写法）</a></li><li class="sidebar-sub-header"><a href="/03.Software/01.DataStructureAndAlgorithm/SkillLibrary/Part03.DFS%E5%92%8CBFS%E5%92%8C%E5%9B%BE%E8%AE%BA%E6%8A%80%E5%B7%A7.html#_1-2-邻接矩阵版（栈写法）" class="sidebar-link">1.2.邻接矩阵版（栈写法）</a></li><li class="sidebar-sub-header"><a href="/03.Software/01.DataStructureAndAlgorithm/SkillLibrary/Part03.DFS%E5%92%8CBFS%E5%92%8C%E5%9B%BE%E8%AE%BA%E6%8A%80%E5%B7%A7.html#_1-3-邻接表版（队列写法）" class="sidebar-link">1.3.邻接表版（队列写法）</a></li></ul></li><li><a href="/03.Software/01.DataStructureAndAlgorithm/SkillLibrary/Part03.DFS%E5%92%8CBFS%E5%92%8C%E5%9B%BE%E8%AE%BA%E6%8A%80%E5%B7%A7.html#_02-bfs模板⭐️" class="sidebar-link">02.BFS模板⭐️</a><ul class="sidebar-sub-headers"></ul></li><li><a href="/03.Software/01.DataStructureAndAlgorithm/SkillLibrary/Part03.DFS%E5%92%8CBFS%E5%92%8C%E5%9B%BE%E8%AE%BA%E6%8A%80%E5%B7%A7.html#_03-图论模板" class="sidebar-link">03.图论模板</a><ul class="sidebar-sub-headers"></ul></li><li><a href="/03.Software/01.DataStructureAndAlgorithm/SkillLibrary/Part03.DFS%E5%92%8CBFS%E5%92%8C%E5%9B%BE%E8%AE%BA%E6%8A%80%E5%B7%A7.html#_04-二分图-网络流" class="sidebar-link">04.二分图&amp;网络流</a><ul class="sidebar-sub-headers"></ul></li></ul></div></li></ul> </div> <div class="page"> <div class="content"><h1 id="dfs-bfs和图论『模板』"><a href="#dfs-bfs和图论『模板』" class="header-anchor">#</a> DFS/BFS和图论『模板』</h1> <blockquote><p>蓝桥杯A组、CSP第4题</p></blockquote> <div class="language-txt line-numbers-mode"><pre class="language-text"><code>- ⭐️一、DFS模板
- 💬二、BFS摸版
- 🍀三、图论模板
- 01.DFS和BFS模板
- 02.最短路径
- 03.网络流
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br></div></div><h2 id="📑-目录"><a href="#📑-目录" class="header-anchor">#</a> 📑 目录</h2> <p>[TOC]</p> <ul><li>BFS的和树的层次遍历或者先序遍历结合理解</li></ul> <h2 id="_01-dfs模板⭐️"><a href="#_01-dfs模板⭐️" class="header-anchor">#</a> 01.DFS模板⭐️</h2> <ul><li>最抽象并且易懂的模板在《算法笔记》的P352的DFS伪代码，统率了两种存储方式的解法。</li></ul> <h3 id="_1-1-邻接矩阵版（递归写法）"><a href="#_1-1-邻接矩阵版（递归写法）" class="header-anchor">#</a> 1.1.邻接矩阵版（递归写法）</h3> <ul><li><p>1、节点数需要小于等于1000，因为这样开的二维数组int的1e6，几乎就差不多了，再开大就不OK，需要借助“邻接表”</p></li> <li><p>2、递归写法</p></li></ul> <div class="language-cpp line-numbers-mode"><pre class="language-cpp"><code><span class="token macro property"><span class="token directive-hash">#</span><span class="token directive keyword">include</span><span class="token string">&lt;bits/stdc++.h&gt;</span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>

<span class="token comment">//邻接矩阵最大顶点数 </span>
<span class="token keyword">static</span> <span class="token keyword">const</span> <span class="token keyword">int</span> maxn<span class="token operator">=</span><span class="token number">1000</span><span class="token operator">+</span><span class="token number">5</span><span class="token punctuation">;</span>
<span class="token keyword">static</span> <span class="token keyword">const</span> <span class="token keyword">int</span> INF<span class="token operator">=</span><span class="token number">0x3f3f3f</span><span class="token punctuation">;</span>

<span class="token comment">//实际顶点数</span>
<span class="token keyword">int</span> n<span class="token punctuation">;</span>
<span class="token comment">//邻接矩阵存的图</span>
<span class="token keyword">int</span> G<span class="token punctuation">[</span>maxn<span class="token punctuation">]</span><span class="token punctuation">[</span>maxn<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token comment">//也可以是bool vis[maxn]={false},标记是否访问的标记数组</span>
<span class="token keyword">bool</span> vis<span class="token punctuation">[</span>maxn<span class="token punctuation">]</span><span class="token operator">=</span><span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span>

<span class="token comment">//递归DFS </span>
<span class="token keyword">void</span> <span class="token function">DFS</span><span class="token punctuation">(</span><span class="token keyword">int</span> current<span class="token punctuation">,</span> <span class="token keyword">int</span> depth <span class="token punctuation">)</span>
<span class="token punctuation">{</span>
	vis<span class="token punctuation">[</span>current<span class="token punctuation">]</span><span class="token operator">=</span><span class="token boolean">true</span><span class="token punctuation">;</span>
	<span class="token comment">//框架 ———对当前节点current进行的操作，在这进行</span>
	
	<span class="token comment">//枚举从current出发能到达的顶点 </span>
	<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> v<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> v<span class="token operator">&lt;</span>n<span class="token punctuation">;</span> <span class="token operator">++</span>v<span class="token punctuation">)</span>
	<span class="token punctuation">{</span>
		<span class="token keyword">if</span><span class="token punctuation">(</span> <span class="token boolean">false</span><span class="token operator">==</span>vis<span class="token punctuation">[</span>v<span class="token punctuation">]</span> <span class="token operator">&amp;&amp;</span> INF<span class="token operator">!=</span>G<span class="token punctuation">[</span>current<span class="token punctuation">]</span><span class="token punctuation">[</span>v<span class="token punctuation">]</span> <span class="token punctuation">)</span>
		<span class="token punctuation">{</span>
			<span class="token function">DFS</span><span class="token punctuation">(</span>v<span class="token punctuation">,</span>depth<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
		<span class="token punctuation">}</span>
	<span class="token punctuation">}</span>
<span class="token punctuation">}</span>


<span class="token comment">//遍历图 </span>
<span class="token keyword">void</span> <span class="token function">DFSTrave</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
	<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> current<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> current<span class="token operator">&lt;</span>n<span class="token punctuation">;</span> <span class="token operator">++</span>current <span class="token punctuation">)</span>
	<span class="token punctuation">{</span>
		<span class="token keyword">if</span><span class="token punctuation">(</span> <span class="token boolean">false</span><span class="token operator">==</span>vis<span class="token punctuation">[</span>current<span class="token punctuation">]</span> <span class="token punctuation">)</span>
		<span class="token punctuation">{</span>
			<span class="token function">DFS</span><span class="token punctuation">(</span>current<span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span><span class="token comment">//访问current和它所在连通块，1表示DFS的第1层 </span>
		<span class="token punctuation">}</span>
	<span class="token punctuation">}</span>
<span class="token punctuation">}</span> 


<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
	<span class="token comment">//输入图，并且将无法到达的地方设置权值为INF</span>
    <span class="token function">DFSTrave</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
    
	<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span> 
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br><span class="line-number">42</span><br><span class="line-number">43</span><br><span class="line-number">44</span><br><span class="line-number">45</span><br><span class="line-number">46</span><br><span class="line-number">47</span><br><span class="line-number">48</span><br><span class="line-number">49</span><br><span class="line-number">50</span><br><span class="line-number">51</span><br></div></div><h3 id="_1-2-邻接矩阵版（栈写法）"><a href="#_1-2-邻接矩阵版（栈写法）" class="header-anchor">#</a> 1.2.邻接矩阵版（栈写法）</h3> <ul><li><a href="https://leetcode-cn.com/problems/deepest-leaves-sum/solution/stack-c-dfs-by-force-keng/" target="_blank" rel="noopener noreferrer">力扣上模板?????????????<svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg></a></li></ul> <div class="language-cpp line-numbers-mode"><pre class="language-cpp"><code><span class="token keyword">void</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token keyword">int</span> now<span class="token punctuation">)</span>
<span class="token punctuation">{</span>
	vis<span class="token punctuation">[</span>now<span class="token punctuation">]</span><span class="token operator">=</span><span class="token number">1</span><span class="token punctuation">;</span>
	<span class="token comment">//Balabala1</span>
	<span class="token keyword">for</span> <span class="token punctuation">(</span>每一条now出发的边<span class="token punctuation">)</span>
	<span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token operator">!</span>vis<span class="token punctuation">[</span>e<span class="token punctuation">.</span>to<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token function">dfs</span><span class="token punctuation">(</span>e<span class="token punctuation">.</span>to<span class="token punctuation">)</span><span class="token punctuation">;</span>
	<span class="token comment">//Balabala2 </span>
<span class="token punctuation">}</span>
调用<span class="token function">dfs</span><span class="token punctuation">(</span>Start<span class="token punctuation">)</span>

改成 

<span class="token keyword">void</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
	stack<span class="token punctuation">[</span>top<span class="token operator">=</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">=</span>Start<span class="token punctuation">;</span>
	<span class="token keyword">while</span><span class="token punctuation">(</span>top<span class="token punctuation">)</span>
	<span class="token punctuation">{</span>
		<span class="token keyword">int</span> now<span class="token operator">=</span>stack<span class="token punctuation">[</span>top<span class="token punctuation">]</span><span class="token punctuation">;</span>
		<span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token operator">!</span>vis<span class="token punctuation">[</span>now<span class="token punctuation">]</span><span class="token punctuation">)</span>
		<span class="token punctuation">{</span>
			vis<span class="token punctuation">[</span>now<span class="token punctuation">]</span><span class="token operator">=</span><span class="token number">1</span><span class="token punctuation">;</span>
			<span class="token comment">//Balabala1;</span>
			<span class="token keyword">for</span> <span class="token punctuation">(</span>每一条now出发的边<span class="token punctuation">)</span>
			<span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token operator">!</span>vis<span class="token punctuation">[</span>e<span class="token punctuation">.</span>to<span class="token punctuation">]</span><span class="token punctuation">)</span> stack<span class="token punctuation">[</span><span class="token operator">++</span>top<span class="token punctuation">]</span><span class="token operator">=</span>e<span class="token punctuation">.</span>to<span class="token punctuation">;</span>
		<span class="token punctuation">}</span>
		<span class="token keyword">else</span>
		<span class="token punctuation">{</span>
			<span class="token comment">//Balabala2;</span>
			top<span class="token operator">--</span><span class="token punctuation">;</span>
		<span class="token punctuation">}</span>
	<span class="token punctuation">}</span>
<span class="token punctuation">}</span>

作者：陈诗翰
链接：https<span class="token operator">:</span><span class="token comment">//www.zhihu.com/question/22985195/answer/29274088</span>
来源：知乎
​
陈诗翰
陈诗翰 <span class="token punctuation">(</span>作者<span class="token punctuation">)</span> 回复赵奕<span class="token number">2016</span><span class="token operator">-</span><span class="token number">06</span><span class="token operator">-</span><span class="token number">22</span>
好像是的喔<span class="token number">2333</span>
​赞
赵奕
赵奕回复陈诗翰 <span class="token punctuation">(</span>作者<span class="token punctuation">)</span><span class="token number">2016</span><span class="token operator">-</span><span class="token number">06</span><span class="token operator">-</span><span class="token number">22</span>
貌似把那个<span class="token keyword">for</span>循环倒过来跑一遍就可以了？
​赞
陈诗翰 <span class="token punctuation">(</span>作者<span class="token punctuation">)</span> 回复赵奕<span class="token number">2016</span><span class="token operator">-</span><span class="token number">06</span><span class="token operator">-</span><span class="token number">22</span>
对的
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br><span class="line-number">42</span><br><span class="line-number">43</span><br><span class="line-number">44</span><br><span class="line-number">45</span><br><span class="line-number">46</span><br><span class="line-number">47</span><br></div></div><h3 id="_1-3-邻接表版（队列写法）"><a href="#_1-3-邻接表版（队列写法）" class="header-anchor">#</a> 1.3.邻接表版（队列写法）</h3> <h4 id="方法1—vector实现版"><a href="#方法1—vector实现版" class="header-anchor">#</a> 方法1—vector实现版</h4> <h4 id="方法2—链表实现版"><a href="#方法2—链表实现版" class="header-anchor">#</a> 方法2—链表实现版</h4> <h2 id="_02-bfs模板⭐️"><a href="#_02-bfs模板⭐️" class="header-anchor">#</a> 02.BFS模板⭐️</h2> <h2 id="_03-图论模板"><a href="#_03-图论模板" class="header-anchor">#</a> 03.图论模板</h2> <h2 id="_04-二分图-网络流"><a href="#_04-二分图-网络流" class="header-anchor">#</a> 04.二分图&amp;网络流</h2> <p>基本知识点：</p> <div class="language-cpp line-numbers-mode"><pre class="language-cpp"><code>假设大家已经会了：
    建图：邻接表<span class="token operator">&amp;</span>链式前向星
    判图连通：并查集
    图的遍历：DFS、BFS
最小生成树：
    Prim算法
    Kruskal算法
最短路：
    SPFA—可以处理有关负权边的图，可以找负环，Bellman<span class="token operator">-</span>Ford算法的队列优化
    Dijkastra算法——堆优化
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br></div></div></div> <div class="page-edit"><!----> <!----></div> <!----> </div> <!----></div></div>
    <script src="/assets/js/app.c70e21ad.js" defer></script><script src="/assets/js/62.76f4b01f.js" defer></script>
  </body>
</html>
